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Proof step 9 from proof refine-read (previous step)

# avol0 = # lpt + m6, avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), avol0[m6 + m8] = mapped(buf1), avol = avol0, buf = buf0, m = m7, m0 = m8, n = n1, n0 = n2, sb = mksb(adr, m1, m2, m3, m4, m5, m6), avol[sb.main + m0].mapped?, sb.main + m0 < # avol, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n0 + n ≤ # buf, m + n ≤ LEB_SIZE, m6 ≤ # avol0, n2 + n1 ≤ # buf0, m7 + n1 ≤ LEB_SIZE, sb.main + m0 < # avol → sb.main + m0 < # avol, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟪ebm_avol_read#(sb.main + m0, m, n0, n, avol; buf; err)⟫ ⟨apersistence_io_read#(m8, m7, n2, n1, adr, m1, log, subarray(avol0, m6, # lpt), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# avol0 = # lpt + m6, avol0[m2] = mapped(buf4), avol0[m3] = mapped(buf3), avol0[0] = mapped(buf2), avol0[m6 + m8] = mapped(buf1), buf = buf0, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-encoded(log, buf4), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf2), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), m6 ≤ # avol0, m7 + n1 ≤ LEB_SIZE, n2 + n1 ≤ # buf0, logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟪ebm_avol_read#(m6 + m8, m7, n2, n1, avol0; buf; err)⟫ ⟨apersistence_io_read#(m8, m7, n2, n1, adr, m1, log, subarray(avol0, m6, # lpt), lpt, orphans; buf0; err0)⟩ (buf = buf0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)